Rearranging Equations – When the Formula has Two Terms that Contain the Subject we Need to Isolate

How do we cope with this unsavoury situation? We do some factorising. Here’s an example of how this is done.

We need to rearrange this equation (formula for the surface area of a box) to isolate b:

A space equals space 2 w b space plus space 2 w h space plus space 2 b h

Our first move is nice and simple; we subtract  2wh from both sides, which gives us:

A space minus space 2 w h space equals space 2 w b space plus space 2 b h

But now we have b in two terms. Here we need to factorise the right side of the equation.

You will remember for any numbers a, b, and c, that:

a(b + c) = ab + ac

So for this equation:

A space minus space 2 w h space equals space 2 w b space plus space 2 b h

Is also:

A space minus space 2 w h space equals space b left parenthesis 2 w space plus space 2 h right parenthesis

It is called factorising because we have found the common factor that both terms divide by (which is b). We could, of course, have also done A minus space 2 w h space equals space 2 left parenthesis w b space plus space b h right parenthesis, but that wouldn’t have helped us!

So from here, we have the simple task of getting left parenthesis 2 w space plus space 2 h right parenthesis spaceover the equals sign by dividing both sides by  left parenthesis 2 w space plus space 2 h right parenthesis, giving us:

b space equals space fraction numerator A space minus space 2 w h over denominator left parenthesis 2 w space plus space 2 h right parenthesis end fraction

To help reinforce what we have just learned, on the next page there are some practice questions. Answers and explanations can be revealed by clicking on show answer.

You have completed 0% of the lesson
0%